Feedback Control Design and Stability Analysis of One Dimensional Evacuation System

Abstract

This paper presents design of nonlinear feedback controllers for two different models representing evacuation dynamics in one dimension. The models presented here are based on the laws of conservation of mass and momentum. The first model is the classical one equation model for a traffic flow based on conservation of mass with a prescribed relationship between density and velocity. The other model is a two equation model in which the velocity is independent of the density. This model is based on conservation of mass and momentum. The equations of motion in both cases are described by nonlinear partial differential equations. We address the feedback control problem for both models. The objective is to synthesize a nonlinear distributed feedback controller that guarantees stability of a closed loop system. The problem of control and stability is formulated directly in the framework of partial differential equations. Sufficient conditions for Lyapunov stability for distributed control are derived